People with sensitive eyes can wear contacts and the contact lenses won't cause damage to the eyes. However, they may experience discomfort. People with sensitive eyes may feel scratchy and dry in the eye. Some may get a red and bloodshot eye with irritation. So people with sensitive eyes may be limited to select some special kinds of contact lenses. If you want to choose contacts for your sensitive eyes, you'd better consult your doctor.
Of course, people with sensitive eyes can wear contact lenses. But they should choose the contacts that are special made for sensitive eyes. And these people shouldn't wear their contact lenses every day. The time they wear contact lenses may be less than those with normal eyes.